Can't try different batteries, this is an FMR, the one with the
non-replacable batteries.

But to answer your question, yes, it can be turned on again and it will
run for an indeterminate amount of time before shutting down again. This
can be repeated several times and is a bit frustrating. I have tried
running the batteries down to nothing and recharging (to see if that helps
them get a complete charge) but that hasn't helped. I've tried this mostly
because I normally leave the unit plugged in, and only occassionally run
it on battery power alone. It's when it is running on battery power that
this occurs, not while plugged in.

Just a quick question out of curiosity. Can you keep running by turning
it on again and again for a long time? I'm wondering if maybe your
batteries were not fully charged? (I've had such problems on my non-FM
recorder when I have rockbox flashed... rockbox measures the battery
status wrong, and stops charging much too soon, as it thinks the battery
is at 100%).